GaN HEMTs with temperature effects

Microelectronics Journal 42 (2011) 923–928

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Microelectronics Journal journal homepage: www.elsevier.com/locate/mejo

Physics-based numerical simulation and device characterizations of AlGaN/GaN HEMTs with temperature effects Hasina F. Huq n, Bashirul Polash Department of Electrical Engineering, The University of Texas-Pan American, Edinburg, TX 78541-2999, USA

a r t i c l e i n f o

abstract

Article history: Received 6 October 2010 Received in revised form 27 January 2011 Accepted 8 February 2011 Available online 9 April 2011

The research presents AlGaN/GaN HEMTs device characterizations at different temperatures using physicsbased numerical simulation. Industry standard simulation tool Silvaco ATLAS is used to characterize the various electronic properties of the device. An extensive theoretical overview is done to achieve the most comprehensive values for GaN and AlGaN properties, as discussed in the paper. This research is mainly focused on simulation of temperature dependent device performances as well as on some other material properties that are not well defined in ATLAS. Energy bandgap, density of states, saturation velocities, surface traps, polarization effect, carrier lifetime and mobility, permittivity, effective Richardson’s constant, and donor and acceptor energy levels are considered as critical parameters for predicting temperature effect in ALGaN/GaN HEMT. Various aspects of device performance are analyzed at high temperature along with the different bias configurations. & 2011 Elsevier Ltd. All rights reserved.

Keywords: AlGaN/GaN HEMT 2-DEG

1. Introduction In recent years, a wide variety of GaN-based FET structures have been reported with a broad spectrum of AlGaN/GaN HEMTs. Advances in materials and device technology in the past years have led to a remarkable rate of progress in the performance available from GaN-based HEMTs. Commercial interests for device development have soared due to such tremendous improvements in device performance. Automotive industries are showing increased interests in GaN HEMTs for high power inverters operating at high ambient temperatures in hybrid vehicles (HVs), electric vehicles (EVs), and fuel cell vehicles (FCVs). After successful deployment of 3 G network for cellular communications, Worldwide Interoperability for Microwave Access (WiMax) technology is now at the peak of interest [1–6]. However, analytical modeling and simulation of device characteristics particularly at high temperatures are not prominent in the literature [1]. It is important to accurately predict device characteristics and performance through simulation prior to fabrication due to high intrinsic cost of the cut-and-try method. Various simulations are conducted on different mechanisms of GaN-based HEMTs such as transport and mobility properties [2,3], selfheating effects [4], carrier lifetime, etc., which enable the understanding of basic device physics. Temperature dependent models for some physical characteristics have been reported by Islam and

n

Corresponding author. E-mail addresses: [email protected] (H.F. Huq), [email protected] (B. Polash).

0026-2692/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2011.02.003

Huq [6]. An integrated simulation of GaN-based devices for performance and characteristics study at high temperatures is greatly emerging. Empirical modeling produces reliable formula that will match existing data, but physics-based simulation predicts device performance based on physical structure, material properties, and bias conditions.

2. Material models specification A set of variables related to the key aspects of device structure are defined first. These are device thickness, source to gate spacing, gate to drain spacing, gate length, device width, and the reference position for the electrodes. A rectangular two-dimensional mesh is specified to create grid points on the device structure for the numerical analysis. A key interest region of the device is the AlGaN/GaN heterojunction where the 2-DEG channel forms. Smaller spacing values are used for the ATLAS ‘mesh’ statement around the AlGaN/GaN interface. The rectangular mesh is assumed within co-ordinates (0, 0), (w, 0), (w, t), and (0, t) where ‘w’ and ‘t’ are device width and thickness, respectively. Once the mesh is specified, materials are assigned throughout the mesh area. For each material type, a region number and corresponding area are specified. Material ‘air’ is used for empty regions. Finally the source, gate, and drain electrodes are specified with their locations. Mesh grids and device structure used in the simulation is shown in Fig. 1. Unlike many other device technologies, no doping statements are used. In AlGaN/GaN-based heterostructures, large spontaneous and piezoelectric polarization fields exist due to the material properties of AlGaN/GaN [6]. Because of this property,

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Fig. 1. Mesh grid, region, materials, and electrode specifications and their locations.

2-DEG is formed with very high sheet carrier concentrations even without any intentional doping. Although the spontaneous polarization is very strong in Group III nitrides, the pyroelectric coefficients, describing the changes in the spontaneous polarization with temperature, are measured to be very small [4,6]. Chang et al. [1] showed that the effect of pyroelectric coefficients on the channel current at high temperature is negligible. The group III-nitride compound material has vast potential for semiconductor applications. However the material properties of III-nitride group are not well established for device modeling [7–9]. Group III-arsenide compound materials are well established within Silvaco for modeling and simulation. BLAZE submodule in ATLAS generally deals with compound semiconductors, but model parameters for nitride based materials are rather limited. Default parameters for various ternary compounds are found in ATLAS manual; however, such information for AlGaN is found to be confined. For the particular device structure, GaN and AlGaN are the key focus of attention. Various parameters are specified for these materials. An extensive theoretical overview is done to achieve the most comprehensive values for GaN and AlGaN properties as discussed in the paper. The temperature dependent material properties such as energy bandgap, density of states, saturation velocities, carrier lifetime and mobility, permittivity, effective Richardson’s constant, donor and acceptors energy levels and ALIGN are analyzed for the simulation. ALIGN specifies the fraction of bandgap difference to be applied on the conduction band discontinuity at the AlGaN/GaN hetero-interface. Specifying appropriate physical models is the most important aspect in ATLAS simulation. For the simulation, the Albrecht [2] mobility models are included for electrons and holes, Shockley–Read– Hall recombination model is used for carrier generation– recombination and lateral electric field-dependent model is used for mobility in biased situation. A thermal contact is specified to derive lattice heating solutions. For temperature dependent impact ionization, Selberherr’s model is chosen [10]. A positive interface charge density value is specified on the AlGaN/GaN boundary. Some of the model parameters are used from the work of various researches [11–13]. A set of numerical methods is selected for the iterative solutions of the model equations to get a

close match when compared to room temperature parameters. These methods include an automated Newton–Richardson procedure, Gummel, block Newton method, and TRAP. TRAP reduces the electrode bias steps taken from the initial approximation if a solution process starts to diverge. An initial solution is performed according to ATLAS specified instruction to include an initial guess for the subsequent solutions. This solution assumes that no external elements are attached to the device. Model equations are solved under various bias conditions and temperatures. Suitable bias voltages are applied at the electrodes to derive separate solutions for drain current vs. gate voltage (Id  Vg) and drain current vs. drain voltage (Id  Vd). Electron concentration plots are analyzed by specifying corresponding parameter on the contours. Accurate profiling of semiconductor devices depends on proper modeling of physical properties. Through the vast researches on GaN-based devices, related material physics and semiconductor basics have been idealized. Simulation of the device is performed by utilizing various material models. Some parameters for simulation are calculated from established physical relationships. Thermal conductivity is determined mainly by electrons thermally excited across the bandgap. Boltzmann distribution describes the probability of an electron making this jump and is proportional to e  (Eg/kbT), where Eg is the energy bandgap (eV), kb is Boltzmann’s constant, and T is the temperature in Kelvin. The most important parameter of any semiconductor material is the energy bandgap. Temperature dependence of energy bandgap (Eg) for a semiconductor can be expressed by the following basic equation: Eg ðTÞ ¼ Eg ð0Þ

aT 2 T þb

ð1Þ

where Eg(0), a, and b are called the fitting parameters. These parameters are estimated from numerous empirical calculations. Values used in this study for GaN and AlN are summarized in Table 1. These selections yield a close match when compared to room temperature energy bandgap values reported in many literatures [14,15]. Energy bandgap for ternary semiconductor is calculated using the values of for the binary compounds and their

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mole fraction according to the following relationship: EgðABÞ ðxÞ ¼ xEgA þ ð1xÞEgB bxð1xÞ

ð2Þ

where x is the mole fraction of the ternary compound. Here b is called the bowing parameter whose value varies among the literatures. For AlxGa1  xN, the bowing parameter value is selected to be 1.3 eV [16]. The number of states at each energy level to be occupied is expressed by density of states (DOS). It is helpful to understand the carrier distribution in a semiconductor material. For any semiconductor material, the general temperature dependence of DOS is   T 3=2 Nc=v ðTÞ ¼ Nc=v ð300Þ ð3Þ 300 where Nc/v(T) is the electron/valence band density of state and T is the temperature in K. The room temperature (300 K) values for GaN, AlN, and AlxGa1  xN are listed in Table 2. The channel is formed in the GaN layer for AlGaN/GaN HEMTs with majority carrier being electrons, a great deal of efforts are Table 1 Fitting parameters for temperature dependent energy bandgap calculation. Eg(0) (eV)

a

b

Source

GaN

3.51

 0.909  10  3

830

[13]

AlN

6.34

 1.799  10  3

1462

[14]

925

seen in literatures to idealize the electron mobility. The Albrecht mobility model has been implemented in this study for electron mobility, which is based on the following relationship [18,19]: (

mn ¼

     )1 T 1:5 T 1:5 1 a lnð1 þ b Þ þb þc 300 300 expðF=TÞ1 2

ð4Þ 4

The fitting parameters a, b, and c are selected to be 1.7  10 , 2.1  10  4, and 1.55  10  2, respectively [20,21]. Temperature dependent mobility for minority carriers in GaN and for both majority and minority carriers in AlN and AlGaN are calculated using a more generic model:

mn ðTÞ ¼ mn ð300Þ

mp ðTÞ ¼ mp ð300Þ



T 300



T 300

1:7 ð5Þ

1:5 ð6Þ

The room temperature mobility parameters are summarized in Table 3. All the units are in m2/(V s). Temperature dependent saturation velocities are modeled using the following relationship [22]: Vsat ðTÞ ¼

Vsat ð300Þ ð1AÞ þ AðT=300Þ

ð7Þ

and for ternary semiconductor materials:

Table 2 Band densities of different materials at room temperature (300 K).

VsatAB ðxÞ ¼ xVsatA ðTÞ þ ð1xÞVsatB ðTÞ þ bxð1xÞ

Nc(3 0 0) (cm  3)

Nv(3 0 0) (cm  3)

Source

GaN AlN

2.23  1018 6.23  1018

4.6  1019 4.88  1020

[17] [17]

Al0.25Ga0.75N

2.71  1018

2.06  1019

Calculated

ð8Þ

where x is the mole fraction and b is the bowing parameter. Values of the fitting parameter A for electrons and holes are 0.44 and 0.59, respectively [22]. Room temperature values of electron and hole mobilities are listed in Table 4 where all the units are in cm/s.

Table 3 Room temperature mobility parameters.

ln(3 0 0)

l p(3 0 0)

Source

GaN AlN

– 135

30 14

[11] [12]

Al0.25Ga0.75N

248

10

[13]

Table 4 Saturation velocities at room temperature. Vsat-n(3 0 0)

Vsat-p(3 0 0)

Source

GaN AlN

2.5  107 1.4  107

1  107 1  107

[13] [14]

Al0.25Ga0.75N

1.7  105

1  107

Calculated

3. Device structure A fragmented section from a wafer containing HEMTs with varying dimensions is used to take measurements (Fig. 2). The test chip has some dummy blocks. Mole fraction of the barrier layer is 0.25. The composition of the layers controls the size of the band discontinuity and quantum well formation in the heterointerface. Concentration of 2-DEG is controlled by the application of gate voltage. The devices have sheet electron concentration ns ¼1.5  1015 cm  3 and electron mobility at room temperature is 1400 cm2/V s. Each sample has two transistors in parallel. Top and bottom horizontal sections are the source pads of the two transistors. Left and right pads in the middle are the gates and drains, respectively. The gate length/width ratios are 2  150, 2  100, and 1  50 mm2.

Fig. 2. Section from a wafer containing AlGaN/GaN HEMTs with varying gate length/width ratio.

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4. Results Various aspects of device performance at high temperatures along with different bias configurations are analyzed. These include 2-DEG concentration, maximum drain current, threshold voltage, input transfer function, and output characteristic curves. The device structure is simulated in the temperature range of 300–600 K. The 2-DEG channel forms at the AlGaN/GaN boundary (0.525 m) into the GaN region (Fig. 3a). A cutline through the gate region is selected and electron concentration value is plotted. It is found that the value increased slightly with the increase in temperatures (Fig. 3b) at a fixed depth (0.02 m) from the AlGaN/ GaN interface. Effects on the 2-DEG channel electron concentration are also analyzed at various bias conditions. At first the gate voltage (Vg) is varied from  5 to 3 V with a constant drain voltage at 0 V. At Vg ¼ 5 V, a below threshold electron concentration is observed and no channel appeared on the AlGaN/GaN interface. However at Vg ¼ 4 V, the channel starts to form. At first the electron concentration increases rapidly but it seemed to be saturated towards the end. Also the drain voltage is varied from

0 to 28 V at 4 V increments with 6 V applied gate voltage (Fig. 4). The electron concentration along the cutline through the gate at a 0.575 m depth is observed. At first the value decreases as the drain voltage is increased, but when Vd ¼16 V or higher, the electron concentration starts to increase. The input transfer and output characteristic functions are simulated at various temperatures. For input transfer function, the source-drain is held at 0 (zero) potential difference. The gate voltage is set within 6 to 5 V with 1 V increment while the drain-source voltage is ranged between 0 and 20 V. The threshold voltage appears almost unchanged with the increase in temperature (Fig. 5). The maximum drain current is decreased from 110 to 34 mA while the temperature is increased from 300 to 600 K, respectively (Fig. 6). Even with this significant degradation in drain current at increased temperature, it exhibits feasibility of high temperature application where mostly other technology fails. From the diverse category of discrete transistors residing on the wafer segment, several distinct ones are selected for measurement at room temperature. These measurements are shown in Fig. 7. The parameters are in logical agreement with the

Fig. 3. (a) AlGaN/GaN HEMT (electron concentration map at 300 K). (b) Values at the 2-DEG for various temperatures – bottom curve corresponds to values at 300 K while the top curve corresponds to 600 K with each curve at 50 K increment.

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Fig. 4. Output characteristics (Id  Vd) curves.

Fig. 5. Input transfer function and threshold voltages at various temperatures.

Fig. 7. DC transfer and output characteristics curves; (a) measured sample (gate L/W: 2  100 mm2); (b) input transfer function Id  Vg curves: Vg ¼ –6 to 0 V, Vd ¼0 to 16 V at 4 V increments; (c) output characteristic Id  Vd curves: Vd ¼ 0 to 24 V, Vg ¼ –6 to 0 V at 1.5 V increments

Fig. 6. Output characteristic curves at different temperatures.

measurement variables. Discontinuities are observed in some of the I–V curves. The most likely cause for these discontinuities is the probe leakage that generally happens for rough contact surface.

5. Conclusion Simulation of the AlGaN/GaN HEMT is described in this paper with a discussion on related physical concepts. Various aspects of the Silvaco ATLAS simulation tool are presented here. Calculations of critical physical parameters are also included. Simulations of different performance trends applicable for temperature

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variations are performed and the device characteristics are analyzed. The peak electron concentration along the channel is about 1  1019 cm  3 when the device is turned on. It does not change much with temperature increase. The simulation results are in logical agreement with the measurement variables at room temperature. However, after analyzing the electron concentration map of the cross sectional area in 2-D, an inflated distribution contours when the temperature is increased. Various biasing conditions do not seem to affect the electron distribution, rather the peak electron concentration value has changed slightly. In the ‘off’ state (Vg ¼  5 V), the electron concentration at the channel interface is  1  1015 cm  3, which ranges from 1.5  1018 to 1.5  1019 cm  3 for gate voltage range between  5 and 3 V, respectively. Pinch-off effect is observed in the 2-D cross sectional electron concentration map as the drain voltage is increased. It suggests that at high voltage, the device may exhibit gate leakage through the substrate [23]. The maximum drain current is decreased while the temperature is increased from 300 to 600 K, respectively. However, the degradation and reliability problems of GaN HEMTs are also caused by the trap-related effects and have been a critical issue that is widely discussed in recent years [24].

Acknowledgment The authors would like to extend their gratitude to Dr. Asif Khan of University of South Carolina for supplying the GaN HEMT devices. References [1] Y. Chang, K.Y. Tong, C. Surya, Numerical simulation of current voltage characteristics of AlGaN/GaN HEMTs at high temperatures, Semiconductor Science and Technology 20 (2005) 188. [2] J.D. Albrecht, R.P. Wang, P.P. Ruden, Electron transport characteristics of GaN for high temperature device modeling, Journal of Applied Physics 83 (1998) 4777. [3] Y. Cordier, M. Hugues, P. Lorenzini, F. Semond, F. Natali, J. Massies, Electron mobility and transfer characteristics in AlGaN/GaN HEMTs,, Physica Status Solidi (c) 2 (2005) 2720. [4] V.O. Turina, A.A. Balandin, Electrothermal simulation of the self-heating effects in GaN-based field-effect transistors,, Journal of Applied Physics 100 (2006) 054501.

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